A liability consists of a payment of 2000 to be paid six months from now and a payment of 1500 to be paid one year from now. The only investments available are:

1. Six-month zero-coupon bonds with an annual nominal yield rate of 3.5% convertible semiannually, and
2. One-year par value bonds with an annual coupon rate of 6% payable semiannually and an annual nominal yield rate of 4.2% convertible semiannually.

Calculate the total cost of a portfolio that exactly matches the liability cash flows.

• 3393
• 3404
• 3418
• 3447
• 3463

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: B

The price of a one-year bond for 1000 is [math]\frac{30}{1.021}+\frac{1030}{1.021^2}=1017.45[/math]. Therefore, to match the payment at time 2 we need to invest [math]\frac{1500}{1030} 1017.45=1481.72[/math] in the oneyear bond.

The one-year bond gives a payment of [math]\frac{1500}{1030} 30=43.69[/math] at time 0.5 . Therefore, the amount that needs to be invested in the six month zero coupon bond is [math]=\frac{2000-43.69}{1.0175}=1922.66[/math].

The total cost of the dedicated portfolio is: [math]1481.72+1922.66=3404.38[/math].

Copyright 2023 . The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.